========================================================================
  D2 COMPANION: MEASURED REGGE TRIANGULATION OF SCHWARZSCHILD
  (geometric deficits; the h^4 law is MEASURED here, not assumed)
========================================================================
  r_s = 2.0 (M = 1, G = c = 1), proper window s = 0.8 r_s
  levels n = [4, 6, 8, 10, 12, 14, 16]  (mesh scale h = s/n)

FLAT-SPACE NULL TEST (identity metric, same pipeline):
    n = 6: interior hinges = 16064, max|delta| = 7.11e-15
    [PASS] interior deficits vanish in flat space (threshold 1e-9)

SCHWARZSCHILD SERIES (far window, r0 = 2.0 r_s):
  r in [1.717, 2.283] r_s, Kretschmann K = 1.1719e-02, sqrt(K) = 1.0825e-01
    n =   4: interior hinges =     1232, median|delta| = 2.406e-04, max|delta| = 6.599e-03   (0.0 s)
    n =   6: interior hinges =    16064, median|delta| = 1.033e-04, max|delta| = 3.165e-03   (0.1 s)
    n =   8: interior hinges =    75600, median|delta| = 5.729e-05, max|delta| = 1.852e-03   (0.3 s)
    n =  10: interior hinges =   230144, median|delta| = 3.683e-05, max|delta| = 1.214e-03   (0.7 s)
    n =  12: interior hinges =   549200, median|delta| = 2.501e-05, max|delta| = 8.571e-04   (1.5 s)
    n =  14: interior hinges =  1121472, median|delta| = 1.862e-05, max|delta| = 6.371e-04   (2.7 s)
    n =  16: interior hinges =  2054864, median|delta| = 1.408e-05, max|delta| = 4.921e-04   (4.8 s)

  h/r_s      median|delta|   median|sur|   max|sur|    C3(abs)   C2(signed)        C1(Regge)
  0.2000     2.4058e-04      5.7108e-03     9.3887e-03     2.0686e-08   +1.4303e-08     +3.5896e-05
  0.1333     1.0331e-04      2.6017e-03     4.4956e-03     3.5706e-09   +2.4789e-09     +1.1221e-05
  0.1000     5.7295e-05      1.4821e-03     2.6297e-03     1.0714e-09   +7.4513e-10     +5.4130e-06
  0.0800     3.6829e-05      9.5452e-04     1.7241e-03     4.2670e-10   +2.9706e-10     +3.1785e-06
  0.0667     2.5014e-05      6.7020e-04     1.2171e-03     2.0225e-10   +1.4089e-10     +2.0889e-06
  0.0571     1.8621e-05      4.9389e-04     9.0482e-04     1.0790e-10   +7.5200e-11     +1.4771e-06
  0.0500     1.4083e-05      3.8022e-04     6.9899e-04     6.2720e-11   +4.3725e-11     +1.0995e-06

  Doubling ratios log2[dens(h)/dens(h/2)]:
    n =  4 ->  8:  +4.271
    n =  6 -> 12:  +4.142
    n =  8 -> 16:  +4.094

  MEASURED exponents (least-squares over all levels):
    median|delta|        ~ h^2.04   (power counting: 2)
    |S_RS - S_Regge|/Vol ~ h^4.17   (power counting: 4)

SCHWARZSCHILD SERIES (near-horizon window, r0 = 1.5 r_s):
  r in [1.269, 1.731] r_s, Kretschmann K = 6.5844e-02, sqrt(K) = 2.5660e-01
    n =   4: interior hinges =     1232, median|delta| = 7.882e-04, max|delta| = 1.667e-02   (0.0 s)
    n =   6: interior hinges =    16064, median|delta| = 3.307e-04, max|delta| = 8.081e-03   (0.1 s)
    n =   8: interior hinges =    75600, median|delta| = 1.919e-04, max|delta| = 4.757e-03   (0.3 s)
    n =  10: interior hinges =   230144, median|delta| = 1.213e-04, max|delta| = 3.131e-03   (0.7 s)
    n =  12: interior hinges =   549200, median|delta| = 8.474e-05, max|delta| = 2.216e-03   (1.5 s)
    n =  14: interior hinges =  1121472, median|delta| = 6.162e-05, max|delta| = 1.650e-03   (2.7 s)
    n =  16: interior hinges =  2054864, median|delta| = 4.775e-05, max|delta| = 1.277e-03   (4.8 s)

  h/r_s      median|delta|   median|sur|   max|sur|    C3(abs)   C2(signed)        C1(Regge)
  0.2000     7.8818e-04      1.3429e-02     2.2265e-02     2.8627e-07   +2.0371e-07     +9.0091e-05
  0.1333     3.3066e-04      6.1262e-03     1.0824e-02     4.9480e-08   +3.5547e-08     +2.7793e-05
  0.1000     1.9191e-04      3.5028e-03     6.3840e-03     1.4870e-08   +1.0733e-08     +1.3335e-05
  0.0800     1.2132e-04      2.2928e-03     4.2075e-03     5.9295e-09   +4.2921e-09     +7.8084e-06
  0.0667     8.4741e-05      1.6097e-03     2.9815e-03     2.8133e-09   +2.0402e-09     +5.1238e-06
  0.0571     6.1616e-05      1.1801e-03     2.2246e-03     1.5021e-09   +1.0908e-09     +3.6195e-06
  0.0500     4.7749e-05      9.0870e-04     1.7234e-03     8.7368e-10   +6.3505e-10     +2.6926e-06

  Doubling ratios log2[dens(h)/dens(h/2)]:
    n =  4 ->  8:  +4.267
    n =  6 -> 12:  +4.136
    n =  8 -> 16:  +4.089

  MEASURED exponents (least-squares over all levels):
    median|delta|        ~ h^2.01   (power counting: 2)
    |S_RS - S_Regge|/Vol ~ h^4.17   (power counting: 4)

========================================================================
  Interpretation:
  * The deficit exponent ~2 and residual-density exponent ~4 are the
    D2 power-counting claims, now measured on a real triangulation
    with geometric dihedral angles, not generated by construction.
  * Coefficients are mesh/method dependent (chord-length edges);
    the exponent is the invariant content. Flat-space null test
    confirms zero curvature-independent artifact.
  * Regge -> EH convergence itself stays the external CMS input.
========================================================================